I. P. Androulakis, C. D. Maranas, C. A. Floudas, and A. Bb, ?BB: A global optimization method for general constrained nonconvex problems, Journal of Global Optimization, vol.3, issue.3, pp.337-363, 1995.
DOI : 10.1007/BF01099647

C. Audet, P. Hansen, B. Jaumard, and G. Savard, A branch and cut algorithm for nonconvex quadratically constrained quadratic programming, Mathematical Programming, vol.87, issue.1, pp.131-152, 2000.
DOI : 10.1007/s101079900106

P. Belotti, J. Lee, L. Liberti, F. Margot, and A. Waechter, Branching and bounds tightening techniques for non-convex MINLP, Optimization Methods & Software, pp.597-634, 2009.

J. L. Comba and J. Stolfi, Affine arithmetic and its applications to computer graphics, Proceedings of SIBGRAPI'93 -VI Simpósio Brasileiro de Computação Gráfica e Processamento de Imagens, pp.9-18, 1993.

L. De-figueiredo, Surface intersection using affine arithmetic, Proceedings of Graphics Interface'96, pp.168-175, 1996.

L. De-figueiredo and J. Stolfi, Affine arithmetic: Concepts and applications, Numerical Algorithms, pp.147-158, 2004.

E. D. Dolan and J. J. Moré, Benchmarking optimization software with performance profiles, Mathematical Programming, vol.91, issue.2, pp.201-213, 2002.
DOI : 10.1007/s101070100263
URL : http://arxiv.org/abs/cs/0102001

K. Du and R. B. Kearfott, The cluster problem in multivariate global optimization, Journal of Global Optimization, vol.9, issue.3, p.253265, 1994.
DOI : 10.1007/BF01096455

E. Fitan, F. Messine, and B. Nogarède, The Electromagnetic Actuator Design Problem: A General and Rational Approach, IEEE Transactions on Magnetics, vol.40, issue.3, pp.1579-1590, 2004.
DOI : 10.1109/TMAG.2004.827183

J. Fontchastagner, F. Messine, and Y. Lefevre, Design of Electrical Rotating Machines by Associating Deterministic Global Optimization Algorithm With Combinatorial Analytical and Numerical Models, IEEE Transactions on Magnetics, vol.43, issue.8, pp.3411-3419, 2007.
DOI : 10.1109/TMAG.2007.898907

L. Granvilliers and F. Benhamou, RealPaver: an interval solver using constraint satisfaction techniques, ACM Transactions on Mathematical Software, vol.32, p.138156, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00480813

E. R. Hansen, A generalized interval arithmetic, Lecture Notes in Computer Science, vol.29, pp.7-18, 1975.
DOI : 10.1007/3-540-07170-9_2

E. R. Hansen and W. G. Walster, AN OVERVIEW OF GLOBAL OPTIMIZATION USING INTERVAL ANALYSIS, 2004.
DOI : 10.1016/B978-0-12-505630-4.50021-3

R. Horst and H. Tuy, Global Optimization: Deterministic Approaches, 1996.

C. Jansson, Rigorous Lower and Upper Bounds in Linear Programming, SIAM Journal on Optimization, vol.14, issue.3, pp.914-935, 2003.
DOI : 10.1137/S1052623402416839

R. B. Kearfott, Rigorous Global Search: Continuous Problems, 1996.
DOI : 10.1007/978-1-4757-2495-0

R. B. Kearfott and S. Hongthong, Validated Linear Relaxations and Preprocessing: Some Experiments, SIAM Journal on Optimization, vol.16, issue.2, pp.418-433, 2005.
DOI : 10.1137/030602186

J. Lasserre, Global Optimization with Polynomials and the Problem of Moments, SIAM Journal on Optimization, vol.11, issue.3, pp.796-817, 2001.
DOI : 10.1137/S1052623400366802

Y. Lebbah, C. Michel, and M. Rueher, Efficient Pruning Technique Based on Linear Relaxations, Proceedings of Global Optimization and Constraint Satisfaction, pp.1-14, 2005.
DOI : 10.1007/11425076_1

C. D. Maranas and C. A. Floudas, Global optimization in generalized geometric programming, Computers & Chemical Engineering, vol.21, issue.4, pp.351-369, 1997.
DOI : 10.1016/S0098-1354(96)00282-7

M. C. Markot, J. Fernandez, L. G. Casado, and T. Csendes, New interval methods for constrained global optimization, Mathematical Programming, pp.287-318, 2006.
DOI : 10.1007/s10107-005-0607-2

F. Messine, Extensions of affine arithmetic: Application to unconstrained global optimization, Journal of Universal Computer Science, vol.8, pp.992-1015, 2002.

F. Messine, B. Nogarède, and J. Lagouanelle, Optimal design of electromechanical actuators: a new method based on global optimization, IEEE Transactions on Magnetics, vol.34, issue.1, pp.299-308, 1998.
DOI : 10.1109/20.650361

F. Messine and A. Touhami, A General Reliable Quadratic Form: An Extension of Affine Arithmetic, Reliable Computing, vol.4, issue.3, pp.171-192, 2006.
DOI : 10.1007/s11155-006-7217-4

A. Mitsos, B. Chachuat, and P. I. Barton, McCormick-Based Relaxations of Algorithms, SIAM Journal on Optimization, vol.20, issue.2, pp.573-601, 2009.
DOI : 10.1137/080717341

R. E. Moore, Interval Analysis, 1966.

A. Neumaier, Set of test problems COCONUT

A. Neumaier and O. Shcherbina, Safe bounds in linear and mixed-integer linear programming, Mathematical Programming, vol.99, issue.2, pp.283-296, 2004.
DOI : 10.1007/s10107-003-0433-3

A. Neumaier, O. Shcherbina, W. Huyer, and T. Vinko, A comparison of complete global optimization solvers, Mathematical Programming, vol.99, issue.2, pp.335-356, 2005.
DOI : 10.1007/s10107-005-0585-4

J. Ninin, Optimisation Globale basé sur l'Analyse d'Intervalles: Relaxation affine et limitation de la mémoire, 2010.

S. Perron, Applications jointes de l'optimisation combinatoire et globale, 2004.

H. Ratschek and J. Rokne, New Computer Methods for Global Optimization, 1988.

H. Schichl, M. C. Markt, and A. Neumaier, Exclusion regions for optimization problems, Journal of Global Optimization, vol.33, issue.4, 2014.
DOI : 10.1007/s10898-013-0137-z

H. Schichl and A. Neumaier, Interval Analysis on Directed Acyclic Graphs for Global Optimization, Journal of Global Optimization, vol.149, issue.1&2, pp.541-562, 2005.
DOI : 10.1007/s10898-005-0937-x

H. D. Sherali and W. P. Adams, A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems, 1999.
DOI : 10.1007/978-1-4757-4388-3

J. Stolfi and L. De-figueiredo, Self-Validated Numerical Methods and Applications, Monograph for 21st, Brazilian Mathematics Colloquium, 1997.

M. Tawarmalani and N. V. Sahinidis, Global optimization of mixed-integer nonlinear programs: A theoretical and computational study, Mathematical Programming, vol.99, issue.3, pp.563-591, 2004.
DOI : 10.1007/s10107-003-0467-6

P. Van-hentenryck, L. Michel, and Y. Deville, Numerica: a Modelling Language for Global Optimization, 1997.

X. Vu, D. Sam-haroud, and B. Faltings, Enhancing numerical constraint propagation using multiple inclusion representations, Annals of Mathematics and Artificial Intelligence, vol.33, issue.4, pp.295-354, 2009.
DOI : 10.1007/s10472-009-9129-6